部分纠缠熵的微分形式描述：协变相空间中Killing矢量构造的检验

中文摘要 AI 辅助

比特线（bit thread）表述提供了全息纠缠熵的几何描述，而部分纠缠熵（PEE）和PEE线则针对单个边界点解析了这一结构。鉴于PEE线流可以叠加以重构常规比特线流这一事实，我们引入了PEE线流的微分形式描述。在真空AdS$_3$/CFT$_2$设置中，对于某个区间，我们证明了所得形式的通量再现了已知的纠缠轮廓，从而为所提出的描述提供了一致性检验。随后，我们研究了PEE形式是否可能与由协变相空间（CPS）形式构造的流相关联，可能需通过精确形式改进（exact form improvement）来实现。作为首次检验，我们考虑了Rindler-AdS$_3$中的精确Killing矢量。Rindler参数$a$参数化了一个单参数背景族。在每个$a$值处，将相应背景的Killing矢量代入Iyer-Wald表面电荷形式，并保留所得形式的完整$a$依赖性。我们通过对该表面电荷形式关于$a$积分，定义了一个有限的候选流。对于以中心边界点$r_0=0$为源的反射对称PEE流，我们发现，在变换到Poincaré-AdS$_3$后，没有任何Killing参数的选择能再现已知PEE流的两个分量。这一结果表明，此处所考虑的直接的Killing矢量CPS构造不足以再现中心PEE流。可能的扩展包括精确形式改进、不同的CPS流或更一般的生成元选择。

英文摘要

The bit thread formulation provides a geometric description of holographic entanglement entropy, while partial entanglement entropy (PEE) and PEE threads resolve this structure with respect to individual boundary points. Motivated by the fact that PEE thread flows can be superposed to reconstruct conventional bit thread flows, we introduce a differential form description of PEE thread flow. For an interval in the vacuum AdS$_3$/CFT$_2$ setup, we show that the flux of the resulting form reproduces the known entanglement contour, providing a consistency check of the proposed description. We then investigate whether the PEE form can be related, possibly up to an exact form improvement, to a current constructed from the covariant phase space (CPS) formalism. As a first test, we consider exact Killing vectors in Rindler-AdS$_3$. The Rindler parameter $a$ parametrizes a one-parameter family of backgrounds. At each value of $a$, the Killing vector of the corresponding background is substituted into the Iyer-Wald surface charge form, and the full $a$-dependence of the resulting form is retained. We define a finite candidate current by integrating this surface charge form over $a$. For the reflection-symmetric PEE flow sourced at the central boundary point $r_0=0$, we find that no choice of the Killing parameters reproduces both components of the known PEE flow after transforming to Poincaré-AdS$_3$. This result shows that the direct Killing vector CPS construction considered here is not sufficient to reproduce the central PEE flow. Possible extensions include an exact form improvement, a different CPS current, or a more general choice of generator.

发表机构

• Nanchang University（南昌大学）
• East China University of Technology（华东交通大学）
• Jiangxi Normal University（江西师范大学）

机构由 AI 辅助整理，请以论文原文为准。